# If y = log[x+√(x^2+a^2) show that (x^2 + a^2) +d^2y/dx^2+x(dy/dx)=0.

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If y = log$[\sqrt{x^2+a^2}],$ show that (x2 + a2)$\frac{d^2y}{dx^2}$ + $x\frac{dy}{dx}=0$.

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Given,

y = log$[\sqrt{x^2+a^2}]$

Differentiating again with respect to x, we get